In this section we define maps between skeletal supermanifolds \(\mathcal {M}^{m|q}\)  and \(\mathcal {N}^{n|\ell }\)  (of respective dimensions \(m|q\)  and \(n|\ell \)  and where, in the following applications, we may have \(q=k+L\)  and \(\mathcal {M}^{m|q} = \widetilde{\mathcal {M}}^{m|k}\times \mathbb {R}^{0|L}\) ). The strategy (as in [1]}, [2]}) is the following: rather than defining a map \(\Phi : \mathcal {M}^{m|q}\longrightarrow \mathcal {N}^{n|\ell }\)  directly we set how it acts on functions by the pull-back (or composition) operation \(f\longmapsto \Phi ^*f = f\circ \Phi \) . We will essentially use the fact that \(\Phi ^*\)  should be a morphism between the two superalgebras \(\mathcal {C}^\infty (\mathcal {M}^{m|q},\mathbb {R})\)  and \(\mathcal {C}^\infty (\mathcal {N}^{n|\ell },\mathbb {R})\) .
